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a(11) = 7 because there are 7 squarefree numbers up to 11: the numbers listed above for 10, plus 10 itself.

a(13) = 8 because the 12 X 12 matrix described in the first comment by Sharon Sela has rank 8. Rows 2,4,8 (the powers of two) are identical, rows 3,9 (the powers of three) are identical, and rows 6 and 12 (same prime factors) are identical. - Geoffrey Critzer, Dec 07 2014